A285565 0-limiting word of the morphism 0->11, 1-> 0110.

0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0

Offset

1

Comments

The morphism 0->11, 1-> 0110 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 11 -> 01100110; if the number of iterations is odd, the 1-word evolves from 0 -> 11 -> 01100110 -> 110110011011110110011011, as in A285568. See A285567 for a connection to the golden ratio.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1, 1, 0}}] &, {0}, 8] (* A285565 *)
Flatten[Position[s, 0]]  (* A285566 *)
Flatten[Position[s, 1]]  (* A285567 *)

Crossrefs

Cf. A285566, A285567, A285568, A285589.

Sequence in context: A246146 A191162 A234046 * A188076 A189011 A189135

Adjacent sequences: A285562 A285563 A285564 * A285566 A285567 A285568

Keyword

nonn,easy

Author

Clark Kimberling, Apr 30 2017

Status

approved